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How do you graph #y=|-3x|+2#?

1 Answer

Answer:

Below.

Explanation:

Here's what the graph #y= |x|# looks like, the base equation without any transformations. Let's call this the base function.

graph{|x| [-10, 10, -5, 5]}

Now let's add the #-3#.

The use of the "||" brackets around the #-3x# makes the function an absolute value function . That means for every #x# value you put in, the #y# value you receive is the same but positive. So, because this equation is #|-3|#, these brackets make it so you can ignore the negative completely.

Adding the #3# in front of the #x# squishes the graph so that every #y# value is #3# times the base function. (Sort of takes a bit to understand that multiplying the way makes the graph squished).

graph{|-3x| [-10, 10, -5, 5]}

Lastly, the #+2# is a vertical shift, which means that you move the graph up by #2#, so instead of starting the V shape at the #(0,0)#, it moves up by #2#.